Noise-controlled oscillations and their bifurcations in coupled phase oscillators

Area of Science:

• Physics
• Nonlinear Dynamics
• Statistical Mechanics

Background:

• Globally coupled oscillators are fundamental in various natural and engineered systems.
• Understanding the influence of noise on oscillator dynamics is crucial for predicting system behavior.
• Previous studies have explored stationary and rotatory regimes in noisy oscillator networks.

Purpose of the Study:

• To derive and analyze dynamical equations for mean field fluctuations in globally coupled stochastic phase oscillators.
• To identify and characterize distinct dynamical regimes based on noise intensity.
• To investigate the emergence of a previously unreported oscillatory regime.

Main Methods:

• Derivation of dynamical equations for the first two cumulants of mean field fluctuations using Gaussian approximation.
• Detailed bifurcation analysis to identify transitions between regimes.
• Numerical simulations of ensembles of coupled stochastic phase oscillators and FitzHugh-Nagumo elements.

Main Results:

• Identified three dynamical regimes: stationary, rotatory, and locally oscillatory (breathing).
• Demonstrated that noise intensity acts as a control parameter for regime transitions.
• The locally oscillatory regime was observed for the first time in this system.
• Similar regimes were found in globally coupled stochastic FitzHugh-Nagumo elements.

Conclusions:

• Noise intensity critically governs the collective dynamics of globally coupled stochastic oscillators.
• The discovery of the locally oscillatory regime expands the understanding of complex dynamics in such systems.
• The findings have implications for modeling diverse systems, from neural networks to Josephson junction arrays.